Question

The rain water from a roof of dimensions 22 m × 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. If the rain water collected from the roof just fill the cylindrical vessel, then find the rainfall in cm.

Answer 1

Given, length of roof = 22 m

And breadth of roof = 20 m

Let the rainfall be a cm.

∴ Volume of water on the roof = `22 xx 20 xx a/100 = (22a)/5 m^3`

Also, we have radius of base of the cylindrical vessel = 1 m

And height of the cylindrical vessel = 3.5 m

∴ Volume of water in the cylindrical vessel when it is just full

= `(22/7 xx 1 xx 1 xx 7/2)`

= 11 m³

Now, volume of water on the roof = Volume of water in the vessel

⇒ `(22a)/5` = 11

∴ a = `(11 xx 5)/22` = 2.5  ...[∵ Volume of cylinder = π × (radius)² × height]

Hence, the rainfall is 2.5 cm